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The free-fall space environment can be simulated on earth by using a test apparatus enjoying the property that its center of mass and center of rotation coincide. Such a condition can be realized by appropriately distributing mass about the center of rotation. This paper describes the mechanization and operation of a system that automatically distributes mass about the test apparatus center of rotation to cause the center of mass to be located within a prescribed distance below the center of rotation. The operating concept for the single-degree-of-freedom simulator is presented. A prototype system was constructed and tested to verify the feasibility of the concept. The system functioned as predicted and test table periods in excess of 60 seconds were obtained.